Question

5. 6. At a local high school 5000 juniors and seniors recently took an aptitude test. The results of the exam were normally distributed with mean - 450 and o = 50. Calculate the following: a. The PERCENT of students to the nearest tenth of a percent that scored over 425 b. The number of students that scored more than 475 c. The probability of a student selected at random having scored between 400 and 575 A statistics instructor recorded the grades of his students on the final exam. The grades are: 65, 72, 85, 92, 60, 52, 75, 79, 80, 89, 50, 59,95,99, 89, 77, 62, 65, 67, 73, 85, 23, 89, 94, 97 a. Construct a stem-and-leaf display. b. Describe the shape of the distribution. c. Deterinine the mode and median of these scores. d. What percentage of the students passed at least a 70). 7 Use the following collection of 30 test scores: 100, 65, 67, 61, 62, 70, 75, 73, 88, 77, 83, 79, 95, 79, 80, 102, 86, 87, 87, 91, 87, 89, 92, 90, 99, 87, 72, 93, 79,52 a. Construct a frequency distribution table using 6 classes: include classes, frequencies, class marks, class boundaries, relative frequencies and relative percentages. b. Find the mean to the nearest tenth and sample standard deviation to the nearest tenth. c. Use the results from part b to determine the Z-score associated with a data value of 79. 8. In a recent poll on education 64% of all college students stay up all night studying for final exams. A professor at a local college says this is too low and wants to test this claim. He surveys 5,000 college students and finds that 3250 have stayed up all night studying for final exams. Which statement can we conclude. Use a -5% a. State the null and alternative hypothesis b. Determine and draw the hypothesis testing model (label everything) c. Determine the critical value(s) and test statistic d. Determine the conclusion
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Answer 1

Total Sooo students e=so mean M = 450 X - Normal distribution z = X-2 la) over uas P(x> 425) = P(2> 425-1 - Plz> 425-459 = P(2>-05) = 1-P12<-05) = (-0.3085 = 0.6915 (P/Xsas) =a615 69.15% 69.2 % b) more than 675 P(x>475) P(x>475) = P(z) 475-450 Plz>0.5) 55 T-(2005) 1-OGUS 50.3085 over 닉 number of students 5000 (0.3085) = 15425 475 n=1543 Pl 400-450 =PHICZ<25)=P(2.25)~P(2.1) = 0.9938 -2587 =68351 'Probablity=0.835 | SFS.WO Za P/400 < X < 575) 50